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nika2105 [10]
2 years ago
12

Translate the sentence into an equation. Seven times the sum of a number and 4 is equal to 9. Use the variable b for the unknown

number.
Mathematics
1 answer:
zzz [600]2 years ago
4 0

Answer:

7 ( b + 4 ) = 9

Step-by-step explanation:

Let the number be = b

It is given that the :

The number is added to 4.

And the value is equal to 9 when it is 7 times the sum of the number, b and 4.

Thus according to the question, the sentence can be translated in equation form as :

7 ( b + 4 ) = 9

Thus in other word, we can say that the addition of (b + 4) when it is multiplied for 7 times, we get the result as 9.

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Answer:

−0.965925826289068

Step-by-step explanation:

sin 255 = −0.965925826289068

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Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p
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General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3

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<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>

Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y

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<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>

Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\

------

<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>

Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\

Conclusion:

The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

178=x^2+3x-y\\ \\ -6=4x-3y

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A consumer charges a $46.92 purchase on a credit card. The card has a daily interest rate of 0.039%. If the consumer pays off th
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the equation a=1/2(b1+b2)h can be used to determine the area, a, of a trapezoid with height, h, and base lengths, b1 and b2. whi
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Answer:

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        2a = (b₁ + b₂)h           Remove parentheses

        2a = b₁h + b₂h           Subtract b₂h from each side

2a - b₂h = b₁h                    Divide each side by h

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